Nonlocal electrodynamics of normal and superconducting films

Abstract

Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modeled and analyzed. The formalism is based on the Maxwell equations and a material current-voltage characteristics, linear for normal metals and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function sourcefield turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain in both Fourier and real space. Next, the dynamical behavior of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic nonlocality implies that induced currents flow in the entire sample [3,4]. Thus, the film behavior is qualitatively different from that of bulks, and magneto-optical imaging (MOI) of thin superconductors has revealed strong piling up of the magnetic field around the sample edges, where values far above H a are reached [5]. At internal boundaries, such as the inner edge of a planar ring, the field can, due to the nonlocal electrodynamics, be in the opposite direction of the applied field [6,7]. Strongly modified behavior is found also in films patterned with regular arrays of small holes (antidots), which tend to guide the flux into the superconductor [8][9][10][11].The response of Ohmic films exposed to varying transverse magnetic fields is also described by nonlocal electrodynamics, but here the material responds linearly. Numerical solutions for strip and disc geometries have shown that the combination of nonlocality and dissipation causes a rapid penetration of a suddenly applied magnetic field [12,13]. Different from superconductors, even regions deep inside an Ohmic film are quickly penetrated by the magnetic field.A phenomenon that involves both the critical-state and Ohmic properties is the occurrence of flux avalanches or flux jumps. These are commonly observed in type-II superconductors at low temperatures, and are caused by a thermomagnetic instability which drives the superconductor from the critical-state to a high resistivity state [14]. The instability is triggered, e.g. by a small temperature fluctuation which reduces the flux pinning locally, and some quantized flux lines, or vortices, will start moving. This creates local heat dissipation and the temperature will increase even further, thus forming a positive feedback loop. The result can be an exponential growth in the temperature and a large-scale runaway of magnetic flux. In superconducting films the thermomagnetic instability is seen by MOI to manifest as abrupt avalanches of mag...

Controllable morphology of flux avalanches in microstructured superconductors

“…This procedure is described in Ref. [36]. All main features of the avalanches occurring on the samples studied here can be properly reproduced by simulations conducted using this strategy.…”

Flux avalanche in a superconducting film with non-uniform critical current density

“…The positive feedback between nonlocal flux diffusion or flux movement and the Joule heat leads to the flux avalanche and its propagation. Considering the temperature-dependent critical current, Vestgarden et al [14,[31][32][33][34] solved Maxwell's equations coupled to the thermal diffusion equation using the fast Fourier transform (FFT) technique. They pointed out that, at low environmental temperatures, the first avalanche would occur in the middle of the long edges.…”

Магнитополевое Усиление Пиннинга Вихрей На Фрактальных Границах Кластеров Высокотемпературных Сверхпроводников

“…При этом сеть слабых связей имеет фрактальную структуру как во всeм объeме образца, так и на грани-цах различных дефектов или включений. Фрактальные свойства были обнаружены во многих меднооксидных высокотемпературных сверхпроводниках (ВТСП) экспе-риментально на основе резистивных измерений [1,2] и прямым наблюдением с помощью магнитооптической техники [3][4][5]. Моделирование свойств меднооксидных ВТСП также возможно с помощью рассмотрения их фрактальных особенностей [6][7][8].…”